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Imaging materials with intermodulation: Studies in multifrequency atomic force microscopy
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.ORCID iD: 0000-0003-0675-974X
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Atomic Force Microscope (AFM) is a tool for imaging surfaces at the microand nano meter scale. The microscope senses the force acting between a surfaceand a tip positioned at the end of a micro-cantilever, forming an image of the surface topography. Image contrast however, arises not only from surface topography, but also from variation in material composition. Improved material contrast, and improved interpretation of that contrast are two issues central to the further development of AFM.

This thesis studies dynamic AFM where the cantilever is driven at multiple frequencies simultaneously. Due to the nonlinear dependence of the tip-surface force on the tip’s position, the cantilever will oscillate not only at the driven frequencies, but also at harmonics and at mixing frequencies of the drives, so-called intermodulation products. A mode of AFM called Intermodulation AFM (ImAFM) is primarily studied, which aims to make use of intermodulation products centered around the resonance frequency of the cantilever. With proper excitation many intermodulation products are generated near resonance where they can be measured with large signal-to-noise ratio.

ImAFM is performed on samples containing two distinct domains of different material composition and a contrast metric is introduced to quantitatively evaluate images obtained at each response frequency. Although force sensitivity is highest on resonance, we found that weak intermodulation response off resonance can show larger material contrast. This result shows that the intermodulation images can be used to improve discrimination of materials.

We develop a method to obtain material parameters from multifrequency AFM spectra by fitting a tip-surface force model. Together with ImAFM, this method allows high resolution imaging of material parameters. The method is very generalas it is not limited to a specific force model or particular mode of multifrequency AFM. Several models are discussed and applied to different samples. The parameter images have a direct physical interpretation and, if the model is appropriate, they can be used to relate the measurement to material properties such as the Young’s modulus. Force reconstruction is tested with simulations and on measured data. We use the reconstructed force to define the location of the surface so that we can address the issue of separating topographic contrast and material contrast.

Abstract [sv]

Svepkraftmikroskop (eller atomkraftmikroskop från engelskans atomic forcemicroscope, AFM) är ett instrument för att avbilda ytor på mikro- och nanometer skalan. Mikroskopet känner av kraften som verkar mellan en yta och en spetsplacerad längst ut på ett mikrometerstort fjäderblad och kan därigenom skapa en topografisk bild av ytans form. Bildkontrast uppstår dock inte bara från ytans form utan även från variation i material. Förbättrad materialkontrast och förbättrad tolkning av denna kontrast är två centrala mål i vidareutvecklingen av AFM.

Denna avhandling berör dynamisk AFM där fjädern drivs med flera frekvensersamtidigt. På grund av det ickelinjära förhållandet i yt-spets-kraften som funktion av spetsens position så kommer fjädern inte bara att svänga på de drivna frekvenserna utan också på övertoner och blandfrekvenser, så kallade intermodulationsprodukter. Vi undersöker primärt Intermodulation AFM (ImAFM) som ämnar att utnyttja intermodulationsprodukter nära fjäderns resonansfrekvens. Med en lämplig drivsignal genereras många intermodulationsprodukter nära resonansen, där de kan mätas med bra signal till brus förhållande.

ImAFM utförs på ytor bestående av två distinkta domäner av olika material ochen kontrastmetrik introduceras för att kvantitativt utvärdera bilderna som skapas vid varje frekvens. Trots att känsligheten för kraftmätningen är högst på resonans-frekvensen, så fann vi att svaga intermodulationsprodukter bortanför resonansen kan visa hög materialkontrast. Detta resultat visar att intermodulationsbilderna kan användas för att bättre särskilja olika material.

Vi har utvecklat en metod för att rekonstruera yt-spets-kraften från multifrekventa AFM spektra genom modellanpassning i frekvensrymden. Tillsammans med ImAFM leder detta till högupplösta bilder av materialparametrar. Metoden är generell och är applicerbar för olika kraftmodeller och AFM-varianter. Parametrarna har en direkt fysikalisk tolkning och, om lämpliga modeller används, kan egenskaper så som materialets elasticitetsmodul mätas. Metoden har testats på simulerat såvälsom experimentellt data, och den har också används för att särskilja topografisk kontrast från materialkontrast.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , vi, 104 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2015:02
Keyword [en]
atomic force microscopy, nonlinear dynamics, frequency mixing, force reconstruction
National Category
Nano Technology
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-159689ISBN: 978-91-7595-437-0 (print)OAI: oai:DiVA.org:kth-159689DiVA: diva2:786898
Public defence
2015-02-27, sal FD5, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20150209

Available from: 2015-02-09 Created: 2015-02-06 Last updated: 2015-02-09Bibliographically approved
List of papers
1. Model-based extraction of material properties in multifrequency atomic force microscopy
Open this publication in new window or tab >>Model-based extraction of material properties in multifrequency atomic force microscopy
2012 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 85, no 19, 195449- p.Article in journal (Refereed) Published
Abstract [en]

We present a method to reconstruct the nonlinear tip-surface force and extract material properties from a multifrequency atomic force microscopy (AFM) measurement with a high-quality-factor cantilever resonance. In a measurement time of similar to 2 ms, we are able to accurately reconstruct the tip-surface force-displacement curve, allowing simultaneous high-resolution imaging of both topography and material properties at typical AFM scan rates. We verify the method using numerical simulations, apply it to experimental data, and use it to image mechanical properties of a polymer blend. We further discuss the limitations of the method and identify suitable operating conditions for AFM experiments.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-98006 (URN)10.1103/PhysRevB.85.195449 (DOI)000304395300007 ()2-s2.0-84861707952 (Scopus ID)
Funder
Swedish Research Council
Note
QC 20120618Available from: 2012-06-18 Created: 2012-06-18 Last updated: 2017-12-07Bibliographically approved
2. The role of nonlinear dynamics in quantitative atomic force microscopy
Open this publication in new window or tab >>The role of nonlinear dynamics in quantitative atomic force microscopy
2012 (English)In: Nanotechnology, ISSN 0957-4484, E-ISSN 1361-6528, Vol. 23, no 26, 265705- p.Article in journal (Refereed) Published
Abstract [en]

Various methods of force measurement with the atomic force microscope are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilever's fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.

National Category
Nano Technology
Identifiers
urn:nbn:se:kth:diva-99062 (URN)10.1088/0957-4484/23/26/265705 (DOI)000305411400017 ()2-s2.0-84862638379 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20120719

Available from: 2012-07-19 Created: 2012-07-13 Last updated: 2017-12-07Bibliographically approved
3. Simultaneous imaging of surface and magnetic forces
Open this publication in new window or tab >>Simultaneous imaging of surface and magnetic forces
2013 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 103, no 1, 013114- p.Article in journal (Refereed) Published
Abstract [en]

We demonstrate quantitative force imaging of long-range magnetic forces simultaneously with near-surface van-der-Waals and contact-mechanics forces using intermodulation atomic force microscopy. Magnetic forces at the 200 pN level are separated from near-surface forces at the 30 nN level. Imaging of these forces is performed in both the contact and non-contact regimes of near-surface interactions.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2013
Keyword
Magnetic force, Non-contact, Quantitative forces, Simultaneous imaging
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-125561 (URN)10.1063/1.4812979 (DOI)000321497200041 ()2-s2.0-84880266176 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20130812

Available from: 2013-08-12 Created: 2013-08-09 Last updated: 2017-12-06Bibliographically approved
4. Interpreting motion and force for narrow-band intermodulation atomic force microscopy
Open this publication in new window or tab >>Interpreting motion and force for narrow-band intermodulation atomic force microscopy
2013 (English)In: Beilstein Journal of Nanotechnology, ISSN 2190-4286, Vol. 4, 45-56 p.Article in journal (Refereed) Published
Abstract [en]

Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with the tip motion (F-I) and quadrature to the motion (F-Q). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F-I and F-Q actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F-I and F-Q from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F-I and F-Q, providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.

Keyword
atomic force microscopy, AFM, frequency combs, force spectroscopy, high-quality-factor resonators, intermodulation, multifrequency
National Category
Nano Technology
Identifiers
urn:nbn:se:kth:diva-118243 (URN)10.3762/bjnano.4.5 (DOI)000313722200001 ()2-s2.0-84876109153 (Scopus ID)
Note

QC 20130214

Available from: 2013-02-14 Created: 2013-02-14 Last updated: 2015-02-09Bibliographically approved
5. Determining surface properties with bimodal and multimodal AFM
Open this publication in new window or tab >>Determining surface properties with bimodal and multimodal AFM
2014 (English)In: Nanotechnology, ISSN 0957-4484, E-ISSN 1361-6528, Vol. 25, no 48, 485708- p.Article in journal (Refereed) Published
Abstract [en]

Conventional dynamic atomic force microscopy (AFM) can be extended to bimodal and multimodal AFM in which the cantilever is simultaneously excited at two or more resonance frequencies. Such excitation schemes result in one additional amplitude and phase images for each driven resonance, and potentially convey more information about the surface under investigation. Here we present a theoretical basis for using this information to approximate the parameters of a tip-surface interaction model. The theory is verified by simulations with added noise corresponding to room-temperature measurements.

Keyword
atomic force microscopy, multifrequency AFM, surface properties
National Category
Nano Technology
Identifiers
urn:nbn:se:kth:diva-158801 (URN)10.1088/0957-4484/25/48/485708 (DOI)000345286400024 ()2-s2.0-84911091674 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20150204

Available from: 2015-02-04 Created: 2015-01-12 Last updated: 2017-12-05Bibliographically approved
6. Improving image contrast and material discrimination with nonlinear response in bimodal atomic force microscopy
Open this publication in new window or tab >>Improving image contrast and material discrimination with nonlinear response in bimodal atomic force microscopy
2015 (English)In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 6, 6270Article in journal (Refereed) Published
Abstract [en]

Atomic force microscopy has recently been extented to bimodal operation, where increased image contrast is achieved through excitation and measurement of two cantilever eigenmodes. This enhanced material contrast is advantageous in analysis of complex heterogeneous materials with phase separation on the micro or nanometre scale. Here we show that much greater image contrast results from analysis of nonlinear response to the bimodal drive, at harmonics and mixing frequencies. The amplitude and phase of up to 17 frequencies are simultaneously measured in a single scan. Using a machine-learning algorithm we demonstrate almost threefold improvement in the ability to separate material components of a polymer blend when including this nonlinear response. Beyond the statistical analysis performed here, analysis of nonlinear response could be used to obtain quantitative material properties at high speeds and with enhanced resolution.

Keyword
Mode, Cantilevers, Resolution, Energy, AFM
National Category
Nano Technology
Identifiers
urn:nbn:se:kth:diva-159699 (URN)10.1038/ncomms7270 (DOI)000350289500001 ()25665933 (PubMedID)2-s2.0-84955294610 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20150211

Available from: 2015-02-09 Created: 2015-02-09 Last updated: 2017-12-04Bibliographically approved

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